Pentagons Inside Pentagon

Geometry Level 4

Inside a regular pentagon \(ABCDE\), construct 5 more regular pentagons of side length \(\dfrac{1}{2}AB\). The part of the overlapping of these pentagons yields another regular pentagon of side length \(MN\).

Let \(r=\dfrac{AB}{MN}\). Find \(\displaystyle \left \lfloor 1000r \right \rfloor\).

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